By Toshiyuki Shiozawa

ISBN-10: 3642058345

ISBN-13: 9783642058349

ISBN-10: 3662062615

ISBN-13: 9783662062616

*Waves in Relativistic Electron Beams *presents a sophisticated process classical electrodynamics with software to the iteration of high-power coherent radiation within the microwave to optical-wave areas. in particular, it offers readers with the fundamentals of complex electromagnetic conception and relativistic electrodynamics, guiding them step-by-step during the concept of free-electron lasers. The theoretical remedy all through this publication is totally built via the standard third-dimensional vector calculus. This booklet should be suggested as a graduate-level textbook or a reference e-book within the fields of complex electromagnetic concept, relativistic electrodynamics, beam physics and plasma sciences.

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**Additional info for Classical Relativistic Electrodynamics: Theory of Light Emission and Application to Free Electron Lasers**

**Example text**

1 ) corresponds to the force exerted on a unit charge by an electromagnetic field at a point on the closed contour C moving with velocity v. 1) is equal to the total work done o n a unit charge by the field when it is carried aro und the closed conto ur C. This work is, by definition , the electro m otive fo rce induced along the closed contour C . 1 ) s ------------<------------ .. ·, / v c Fig. 2. 6 Integral Representation of the Maxwell Equations 49 includes not only the temporal change of B itself but also the change of the magnetic flux due to the motion of the contour C.

6), as i(w')=ut: 0 [1- 2( w~ y w-v·k f]=i(w-v·k). 9). 4R 2. 6 Integral Representation of the Maxwell Equations in Moving Systems Consider a closed contour C moving with constant velocity v relative to the inertial system /, and an open surface S bounded by the closed contour C, as shown in Fig. 2. Then, let us discuss the integral representation of the Maxwell equations for the closed contour C and the open surface S. First, we consider Faraday's induction law, which states that if the amo unt of the magnetic flux linking the closed contour C is temporally changed, the electromotive force is produced around C with the magnitude equal to the negative time rate of change of the magnetic flux linking the contour C.

Then the value of the phase is kept invariant if viewed from the system/'. In other words, the phase is an invariant under the Lorentz transformation. The in variance of the phase is expressed as wt- k · r = w't'- k' · r'. 2) 46 2. Foundations of Relativistic Electrodynamics wt- (k,x + k,y + kc:) = w't'- (k;x' + k;y' + (:'). 8), we recognize that the components of the wave vector k are transformed like the spatial coordinates and w/c 2 like the temporal coordinate. 6), we can find how the wavelength and the direction of propagation of a plane wave change when we move from one inertial frame to another.

### Classical Relativistic Electrodynamics: Theory of Light Emission and Application to Free Electron Lasers by Toshiyuki Shiozawa

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